On the Galois Lattice of Bipartite Distance Hereditary Graphs
We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a Bipartite Distance Hereditary graph. We show that the lattice can be realized as the containment relation among directed paths in an arborescence. Moreover, a compact encoding of Bipartite Distance Hereditary graphs is proposed, that allows optimal time computation of neighborhood intersections and maximal bicliques.
KeywordsGalois lattice Transitive reduction Distance hereditary graph Ptolemaic graph
- 11.Howorka, E.: A characterization of Ptolemaic graphs, survey of results. In: Proceedings of the 8th SE Conference Combinatorics, Graph Theory and Computing, pp. 355–361 (1977)Google Scholar